It has been realized in recent years that chiral effective field theory (EFT) [1]}, [2]}, [3]}, [4]}, [5]}, [6]}
can play a central role in addressing these uncertainties. Nuclear structure, ab-initio calculations based on chiral-EFT interactions [7]}, [8]}, [9]}
have recently become available for some phenomenologically relevant nuclei [10]}, [11]}, [12]}. In addition,
the issue of \(g_A\)  quenching in single \(\beta \)  decays has been demonstrated to arise from the combination of two-nucleon
weak currents and strong correlations in the nucleus [13]}, [14]}, [15]}, and
the few-nucleon amplitudes used as input in nuclear structure calculations have been scrutinized in chiral EFT
for various sources of LNV [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, [24]}, [25]}.
In the context of light-Majorana-neutrino exchange, using
naive dimensional counting, the leading contribution in the chiral-EFT expansion arises from a
neutrino-exchange diagram, in which the LNV arises from insertion of the \(\Delta L=2\)  effective neutrino mass \(m_{\beta \beta }\) .
When considering the \(^1S_0\)  channel,
in analogy to the nucleon–nucleon (\(N\!N\) ) potential itself [4]}, [5]}, [6]}
and external currents [29]}, this conclusion no longer holds when demanding manifest renormalizability of the amplitude.
In fact, it has been shown that renormalization requires the promotion of an \(nn\rightarrow ppe^-e^-\)  contact operator to LO [21]}, [24]}, which encodes the exchange of neutrinos with energy/momentum greater than the nuclear scale and thus cannot be resolved in chiral EFT.
As discussed in greater detail in Refs. [24]}, [33]},
the new coupling encodes a non-factorizable two-nucleon effect, beyond the factorizable one-nucleon corrections
captured by the radii of weak form factors, which also give a short-range neutrino
potential. Moreover, the new short-range coupling is not captured by the so-called
short-range correlations [34]}, [35]}, [36]}, [37]},
as it is needed even when one works with fully correlated wave functions, i.e., exact solutions of
the Schrödinger equation with the appropriate strong potential.
The situation is analogous to single \(\beta \)  decay, where two-nucleon weak currents and short-range correlations
are both present, and the combination of both
leads to the apparent quenching of \(g_A\)  [14]}, [15]}.
